limits of sequences with ln(n)

I have a problem with these sequences:

The first one - I don't know how to get rid of the ln(something) function or maybe I'm just doing it in a wrong way. The second one - everything would be great if there wasn't this which I don't know what to do with. The third one - I don't have any idea about this one... I would appreciate your hints or solutions. I've been trying to solve them for so long but I constantly get wrong answers (I used wolfram alpha).

Re: limits of sequences with ln(n)

Originally Posted by Lisa91

I have a problem with these sequences: lim n-> infinity [ln(3n^2+20n+5)]/[ln(n^9-3n+12)] lim n-> ininity (n ln(n^2+1)-2n(lnn)(lnn)^(1/n)) lim n> infinity (1*4*7*...*(3n+1))/(2*5*8*...*(3n+2)) The first one - I don't know how to get rid of the ln(something) function or maybe I'm just doing it in a wrong way. The second one - everything would be great if there wasn't this lnn)(lnn)^(1/n) which I don't know what to do with. The third one - I don't have any idea about this one... I would appreciate your hints or solutions. I've been trying to solve them for so long but I constantly get wrong answers (I used wolfram alpha).

Re: limits of sequences with ln(n)

Yes! I was quite serious.
If you look at the OP before it was edited, you would why.
As you can see it was made readable.

And LaTeX is easy to learn.
If I had my way, all regular posters should be required to us LaTeX code.

Yes, I'm agree with you. I discovered recently , and I try to practice every day because is very useful.

But I mean that is difficult to learn, especially on this page. When I post it's too annoying see the equations combined with the HTML code. I can't see the HTML when I'm editing my code, I don't know why. In other pages I use an editor (in my case use TextMaker) and I only had to copy-paste. But here I have to write everything on one line, and it seems that LaTeX doesn't work well here, sometimes there are mistakes, I have to write "{}" all the time. I don't know if I'm the only one with this problems.

Re: limits of sequences with ln(n)

Thank you very much, guys. I am wondering whether I am allowed to apply the de L'Hospital rule because we have a sequence, not a function here. I think I need to proof that let's say and are differentiable. Is there anyone who's studying math?